Your iPhone and automatic updates are behaving exactly as expected. Automatic updates do not occur immediately.
In more detail, System Software Updates have a phased rollout. You can either manually install the updates when they are released, or allow your device to automatically install the update when the phased auto-rollout begins in your region.
Automatic rollout is intentionally staggered by Apple for two principal reasons:
1) Early adopters who choose to manually install the update when released tend to identify significant unanticipated issues if they should occur. Identified issues, should they occur, may delay the automatic rollout while early issues are resolved.
2) Phased rollout by region and device ensures that Apple's regional update servers are not overwhelmed by ten of millions of devices simultaneously requesting update. While there is significant capacity across Apple's regional server infrastructure, there are still limits to the number of simultaneous connection requests that can be supported at any particular point in time.